A disease has hit a city. The percentage of the population infected t days after the disease...

Question:

A disease has hit a city. The percentage of the population infected t days after the disease arrives is approximated by {eq}p(t) = 11te^{-\frac{t}{8}}{/eq} for {eq}0 \leq t \leq 48{/eq}.

a) After how many days is the percentage of infected people reaches a maximum?

b) What is the maximum percent of the population infected?

Derivative:

To find the maximum population we will first find the time when the population will be maximum and it can be found by first finding the derivative of the function and then putting it equal to 0.

Answer and Explanation:

To find the maximum population we will find the derivative:

{eq}p(t)=11te^{\frac{-t}{8}} {/eq}

Now differentiating it we get:

{eq}p'(t)=11e^{\frac{-t}{8}}-\frac{11t}{8}e^{\frac{-t}{8}}=0\\ t=8 {/eq}

b) Now we will find the population when t=8:

{eq}P=11(8)e^{-1}\\ =32.37 {/eq}


Learn more about this topic:

Loading...
Solving Partial Derivative Equations

from GRE Math: Study Guide & Test Prep

Chapter 14 / Lesson 1
1.5K

Related to this Question

Explore our homework questions and answers library